ABSTRACT
CHAPTER 2
2.1 In tro d u ctio n
Often researchers are in terested in comparing two processes, or two fertiliz ers, or two detergents, or two therapies, etc. D ata are collected on a suitable response variable under two settings and are used to compare the characteris tics. In some cases d a ta are gathered by conducting an experiment using two trea tm ents 011 homogeneous un its or subjects. I11 these experiments treatm ents are random ly assigned to the un its and d a ta are collected on some response variable. This type of experiment is called a s im p le co m p a ra tive s tu d y or a para lle l s tu d y . The two samples are denoted by ( X \ , X 2, • • •, X m ) and (1'j, Y2, . . . , Yn). The
X 's constitu te a random sample on the random variable X , w ith cdf F (.), and the Y ' s make up a random sample 011 the random variable Y, with cdf G(.). We consider two situations: (1) X and Y are discrete variables and (2) X and Y are continuous variables. The testing problem is usually formulated as testing the null hypothesis : F (z) = G(z). for all real z. This hypothesis is called the hom ,ogeneity h yp o th es is . We will also consider the clinical equivalence of two therapies w ith discrete and continuous response variables. As in C hap ter 1, the results for discrete responses are given first, followed by the results for the continuous responses, w ith complete and censored data . Derivation of optimal linear rank sta tistics and ARE of tests are also discussed in th is chapter.
